Cryptarithms or Alphametics are puzzles in cryptic arithmetic
Cryptarithms / Alphametics
The Contest Center
59 DeGarmo Hills Road
Wappingers Falls, NY 12590


       These popular puzzles are called Cryptarithms by the American Cryptogram Association, and Alphametics by the Journal of Recreational Mathematics.
       Whatever you call them, they all work the same way. Each puzzle consists of one or two arithmetic problems, where the digits 0 through 9 have been replaced by letters. Your job is to find the digit that each letter represents.
       Letters always represent the same digit throughout a puzzle, so if N represents 5 in one place, it represents 5 everywhere. Of course, each puzzle uses a different representation. In some cases a digit has been replaced by an asterisk. That may be any digit.
       Unless the rules for a given puzzle state otherwise, each digit is represented by only one letter, each letter represents only one digit, and any digits that appear in the puzzle may also be represented by a letter. For example, in a puzzle COUNTxUP=1234567 any of the letters C,O,U,N,T,P might represent one of the digits 1,2,3,4,5,6,7.


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Short Multiplication
F O U N D
×       A
S K I L L


Long Multiplication
  H E
  I S
H U B
O F  
L A B

Addition
S N O W Y
  L A C E
C L E A R


Additions (contributed by Frank Mrazik)
   M O R E
B O U N C E
     P E R
 O U N C E
E N C O R E
   M O R E
B O U N C E
     P E R
 O U N C E
  P O O R
    M E
    N O
E N C O R E


Addition (contributed by Frank Mrazik)
  W O O D Y
    W O O D
P E C K E R


Addition (contributed by Frank Mrazik)
  G O T T A
  G E T T A
      B I G
W I N N E R


Additions (contributed by Frank Mrazik)
D E A D L Y
    D U L L
E R R A N D
          A
D E A D L Y
    D U L L
E R R A N D


Additions (contributed by Frank Mrazik)
 T H R E E
C H E E R S
 H E R E S
     A
T E A S E R
 T H R E E
C H E E R S
  L O O K
 H E R E S
     A
  C O O L
T E A S E R


Additions (contributed by Frank Mrazik)
  L E T S
 S O L V E
  T H I S
L I T T L E
T E A S E R
    S E E
    O U R
 D O U B L E
T R O U B L E
T E A S E R S


Additions (contributed by Frank Mrazik)
 P I E C E
    B Y
 P I E C E
T E A S E R
P R E T T Y
L I T T L E
T E A S E R


Additions (contributed by Frank Mrazik)
  S I D E
    B Y
  S I D E
     A
 S M A R T
T E A S E R
     I
  S U R E
  L O V E
    T O
 S O L V E
     A
T E A S E R


Additions (contributed by Frank Mrazik)
    T O
 S O L V E
    O R
   N O T
    T O
 S O L V E
   T H E
T E A S E R
    T O
 S O L V E
    O R
   N O T
    T O
 S O L V E
     A
  R A R E
T E A S E R
   D A D
   D A D
  L E T S
   A L L
 S O L V E
     A
  R E A L
  R A R E
T E A S E R


Additions (contributed by Frank Mrazik)
 R O C K E T
S C I E N C E
     I S
     I N
T E A S E R S
 S O L V E
     A
  R A R E
S T R E S S
  F R E E
T E A S E R


Additions (contributed by Frank Mrazik)
   S E E
     A
   N E W
 W I L L Y
 N I L L Y
T E A S E R
   Y E S
  L E T S
   A L L
   T R Y
     A
 F U N N Y
T E A S E R


Addition (contributed by Frank Mrazik)
   S E E
   T H E
  N E A T
 B U N N Y
T E A S E R
    A T
E A S T E R


Addition (contributed by Frank Mrazik)
   W O W
   W O W
   T H E
 W I S H Y
 W A S H Y
T E A S E R


Addition (contributed by Frank Mrazik)
  P A L E
   A L E
  B E E R
  P L U S
 S T O U T
T E A S E R


Short Multiplication
O L D  ×  G E M  =  E X P E R T


Short Multiplication
B I G  ×  S L Y  =  F E L L O W


Short Multiplication
M A N  ×  B I T  =  M O N K E Y


Short Multiplication
B I G  ×  E L F  =  P A R A D E


Short Multiplication
A S K  ×  T H E  =  A M A Z O N


Short Multiplication
A S K  ×  T H E  =  M O R O N S


Short Multiplication (contributed by R. A. Weiss)
S P I R O  ×  7  =  A G N E W


Short Multiplication
N I N E  ×  F O R  ×  E V E R  =  G O G O G O G O G O


Addition (contributed by Frank Mrazik)
    A D D
  S E V E N
  S E V E N
  S E V E N
  S E V E N
  S E V E N
  S E V E N
  S E V E N
  S E V E N
 E L E V E N
 E L E V E N
 E L E V E N
 E L E V E N
   E V E N
H U N D R E D


Addition
 E L E V E N
 L A G E R S
 R E V I V E
G E N E R A L


Addition
 E L E V E N
 L A G E R S
 R E V I V E
      A
 G E N I A L
R E F E R E E


Addition
   S H E
  W I L L
  W A S H
 T H E S E
S H I R T S


Addition (contributed by Frank Mrazik)
  H A V E
      A
 H A P P Y
 H A P P Y
E A S T E R


Addition
  T H I S
    I S
   T H E
   H O T
   H O T
   H O T
 C H I L I
P E P P E R


Addition
   O H I O
 H A W A I I
 K A N S A S
 A L A S K A
I N D I A N A


Addition
C I R C L E
C I R C L E
C I R C L E
S P H E R E


Addition
C I R C L E
C I R C L E
C I R C L E
C I R C L E
S P H E R E


Additions (contributed by Frank Mrazik)
    M Y
M E L L O W
Y E L L O W
T E A S E R
   W O W
    M Y
M E L L O W
Y E L L O W
P U Z Z L E


Addition
 C H I M P
 C H I M P
 C H I M P
B A B O O N
B A B O O N
G I B B O N


Addition
    I D
  L O V E
    T O
 S O L V E
 T H E I R
R I D D L E


Addition
 T O N T O
A N D T H E
  L O N E
R A N G E R



Planets (submitted by Sudipta Das)
       Professor Earth, looking out of his observatory, told his friend Professor Math, "Out there are uncountable planets and stars... (sensing the latter's boredom) Now, did you know that the other planets of our solar system which you can see, are such that if you replace the letters of five of them by digits 0 through 9, then the sum of four of them is equal to the fifth one?"
       Professor Math leapt out of boredom and began to scribble furiously in his notebook. While Professor Math is busy, why don't you try to name these planets, along with the digit denoted by each letter? Assume that leading zeros are not allowed.

Solved by:   Prahlad Lama, Ender Aktulga


Long Multiplication
  * * * *
  ×  * *
 2 * * * 3
1 * * * 4  
* * 5 5 * *


Long Multiplication
       * * * A * * *
       P R O B L E M
       * * * * * * P
      * * * * * * R  
     * * * * * * O   
    * * * * * * B    
  * * * * * * * L     
 * * * * * * * E      
X * P O M P O M       
* * * * * * * * * * * * * *


Two Additions
F A
 T
A L
L I C
 O R
I C E


Fractions #1
Find a solution where the letters representing the digits 0 to 9, in order, spell an ordinary English word. 
 
  O       M       L
 ---  +  ---  +  ---  =  1
 N E     A P     I D


Fractions #2 (contributed by Frank Mrazik)
Find a solution where the letters representing the digits 0 to 9, in order, spell two common English words. 
 
  O       E       Y
 ---  +  ---  +  ---  =  L
 B D     R G     L A


Fractions #3 (contributed by Frank Mrazik) 
 
         HAPPY
A = ----------------
    (4*TH + OF*JULY)


Addition
INTO
ONTO
CANON
INTACT
AMMONIA
OMISSION
DIACRITIC
STATISTICS
ASSOCIATION
ANTIMACASSAR
CONTORTIONIST
NONDISCRIMINATION
CONTRADISTINCTION
MISADMINISTRATION

Powers
HEROLD  =  SHYDOG


LINKS TO OTHER CRYPTARITHM & ALPHAMETICS WEBSITES
Jorge Soares Cryptarithms Online
More Cryptarithms
More Cryptarithms
Giant 10-Letter Cryptarithms


For more Alphametics, and other mathematical puzzles write to
    Journal of Recreational Mathematics
    26 Austin Ave.
    Amityville, NY 11701
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